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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_units.Quantities"></a><a class="link" href="Quantities.html" title="Quantities">Quantities</a>
</h2></div></div></div>
<div class="toc"><dl>
<dt><span class="section"><a href="Quantities.html#boost_units.Quantities.Heterogeneous_Operators">Heterogeneous
      Operators</a></span></dt>
<dt><span class="section"><a href="Quantities.html#boost_units.Quantities.Conversions">Conversions</a></span></dt>
<dt><span class="section"><a href="Quantities.html#boost_units.Quantities.Quantity_Construction_and_Conversion">Construction
      and Conversion of Quantities</a></span></dt>
</dl></div>
<p>
      A <span class="bold"><strong>quantity</strong></span> is defined as a value of an arbitrary
      value type that is associated with a specific unit. For example, while meter
      is a unit, 3.0 meters is a quantity. Quantities obey two separate algebras:
      the native algebra for their value type, and the dimensional analysis algebra
      for the associated unit. In addition, algebraic operations are defined between
      units and quantities to simplify the definition of quantities; it is effectively
      equivalent to algebra with a unit-valued quantity.
    </p>
<p>
      Quantities are implemented by the <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span>
      template class defined in <code class="computeroutput"><a class="link" href="Reference.html#header.boost.units.quantity_hpp" title="Header &lt;boost/units/quantity.hpp&gt;">boost/units/quantity.hpp</a></code>
      :
    </p>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Unit</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">Y</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">class</span> <span class="identifier">quantity</span><span class="special">;</span>
</pre>
<p>
      This class is templated on both unit type (<code class="computeroutput"><span class="identifier">Unit</span></code>)
      and value type (<code class="computeroutput"><span class="identifier">Y</span></code>), with the
      latter defaulting to double-precision floating point if not otherwise specified.
      The value type must have a normal copy constructor and copy assignment operator.
      Operators +, -, *, and / are provided for algebraic operations between scalars
      and units, scalars and quantities, units and quantities, and between quantities.
      In addition, integral and rational powers and roots can be computed using the
      <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/pow_idp109277632.html" title="Function template pow">pow</a></code></span>&lt;R&gt;
      and <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/root.html" title="Function template root">root</a></code></span>&lt;R&gt;
      functions. Finally, the standard set of boolean comparison operators ( <code class="computeroutput"><span class="special">==,</span> <span class="special">!=,</span> <span class="special">&lt;,</span>
      <span class="special">&lt;=,</span> <span class="special">&gt;,</span>
      <span class="keyword">and</span> <span class="special">&gt;=</span></code>
      ) are provided to allow comparison of quantities from the same unit system.
      All operators simply delegate to the corresponding operator of the value type
      if the units permit.
    </p>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_units.Quantities.Heterogeneous_Operators"></a><a class="link" href="Quantities.html#boost_units.Quantities.Heterogeneous_Operators" title="Heterogeneous Operators">Heterogeneous
      Operators</a>
</h3></div></div></div>
<p>
        For most common value types, the result type of arithmetic operators is the
        same as the value type itself. For example, the sum of two double precision
        floating point numbers is another double precision floating point number.
        However, there are instances where this is not the case. A simple example
        is given by the <a href="http://en.wikipedia.org/wiki/Natural_number" target="_top">natural
        numbers</a> where the operator arithmetic obeys the following rules (using
        the standard notation for <a href="http://en.wikipedia.org/wiki/Number" target="_top">number
        systems</a>):
      </p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
            <span class="inlinemediaobject"><img src="../../../libs/units/images/form_12.png" alt="form_12"></span>
          </li>
<li class="listitem">
            <span class="inlinemediaobject"><img src="../../../libs/units/images/form_13.png" alt="form_13"></span>
          </li>
<li class="listitem">
            <span class="inlinemediaobject"><img src="../../../libs/units/images/form_14.png" alt="form_14"></span>
          </li>
<li class="listitem">
            <span class="inlinemediaobject"><img src="../../../libs/units/images/form_15.png" alt="form_15"></span>
          </li>
</ul></div>
<p>
        This library is designed to support arbitrary value type algebra for addition,
        subtraction, multiplication, division, and rational powers and roots. It
        uses Boost.Typeof to deduce the result of these operators. For compilers
        that support <code class="computeroutput"><span class="identifier">typeof</span></code>, the
        appropriate value type will be automatically deduced. For compilers that
        do not provide language support for <code class="computeroutput"><span class="identifier">typeof</span></code>
        it is necessary to register all the types used. For the case of natural numbers,
        this would amount to something like the following:
      </p>
<pre class="programlisting"><span class="identifier">BOOST_TYPEOF_REGISTER_TYPE</span><span class="special">(</span><span class="identifier">natural</span><span class="special">);</span>
<span class="identifier">BOOST_TYPEOF_REGISTER_TYPE</span><span class="special">(</span><span class="identifier">integer</span><span class="special">);</span>
<span class="identifier">BOOST_TYPEOF_REGISTER_TYPE</span><span class="special">(</span><span class="identifier">rational</span><span class="special">);</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_units.Quantities.Conversions"></a><a class="link" href="Quantities.html#boost_units.Quantities.Conversions" title="Conversions">Conversions</a>
</h3></div></div></div>
<p>
        Conversion is only meaningful for quantities as it implies the presence of
        at least a multiplicative scale factor and, possibly, and affine linear offset.
        Macros for simplifying the definition of conversions between units can be
        found in <code class="computeroutput"><a class="link" href="Reference.html#header.boost.units.conversion_hpp" title="Header &lt;boost/units/conversion.hpp&gt;">boost/units/conversion.hpp</a></code>
        and <code class="computeroutput"><a class="link" href="Reference.html#header.boost.units.absolute_hpp" title="Header &lt;boost/units/absolute.hpp&gt;">boost/units/absolute.hpp</a></code>
        (for affine conversions with offsets).
      </p>
<p>
        The macro <span class="underline"><code class="computeroutput"><a class="link" href="../BOOST_UNITS_DEFINE_CONVERSION_FACTOR.html" title="Macro BOOST_UNITS_DEFINE_CONVERSION_FACTOR">BOOST_UNITS_DEFINE_CONVERSION_FACTOR</a></code></span>
        specifies a scale factor for conversion from the first unit type to the second.
        The first argument must be a <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/base_unit.html" title="Class template base_unit">base_unit</a></code></span>.
        The second argument can be either a <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/base_unit.html" title="Class template base_unit">base_unit</a></code></span> or a <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/unit.html" title="Class template unit">unit</a></code></span>.
      </p>
<p>
        Let's declare a simple base unit:
      </p>
<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">foot_base_unit</span> <span class="special">:</span> <span class="identifier">base_unit</span><span class="special">&lt;</span><span class="identifier">foot_base_unit</span><span class="special">,</span> <span class="identifier">length_dimension</span><span class="special">,</span> <span class="number">10</span><span class="special">&gt;</span> <span class="special">{</span> <span class="special">};</span>
</pre>
<p>
        Now, we want to be able to convert feet to meters and vice versa. The foot
        is defined as exactly 0.3048 meters, so we can write the following
      </p>
<pre class="programlisting"><span class="identifier">BOOST_UNITS_DEFINE_CONVERSION_FACTOR</span><span class="special">(</span><span class="identifier">foot_base_unit</span><span class="special">,</span> <span class="identifier">meter_base_unit</span><span class="special">,</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">0.3048</span><span class="special">);</span>
</pre>
<p>
        Alternately, we could use the SI length <code class="computeroutput"><span class="keyword">typedef</span></code>:
      </p>
<pre class="programlisting"><span class="identifier">BOOST_UNITS_DEFINE_CONVERSION_FACTOR</span><span class="special">(</span><span class="identifier">foot_base_unit</span><span class="special">,</span> <span class="identifier">SI</span><span class="special">::</span><span class="identifier">length</span><span class="special">,</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">0.3048</span><span class="special">);</span>
</pre>
<p>
        Since the SI unit of length is the meter, these two definitions are equivalent.
        If these conversions have been defined, then converting between scaled forms
        of these units will also automatically work.
      </p>
<p>
        The macro <span class="underline"><code class="computeroutput"><a class="link" href="../BOOST_UNITS_DEFAULT_CONVERSION.html" title="Macro BOOST_UNITS_DEFAULT_CONVERSION">BOOST_UNITS_DEFAULT_CONVERSION</a></code></span>
        specifies a conversion that will be applied to a base unit when no direct
        conversion is possible. This can be used to make arbitrary conversions work
        with a single specialization:
      </p>
<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">my_unit_tag</span> <span class="special">:</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">base_unit</span><span class="special">&lt;</span><span class="identifier">my_unit_tag</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">force_type</span><span class="special">,</span> <span class="number">1</span><span class="special">&gt;</span> <span class="special">{};</span>
<span class="comment">// define the conversion factor</span>
<span class="identifier">BOOST_UNITS_DEFINE_CONVERSION_FACTOR</span><span class="special">(</span><span class="identifier">my_unit_tag</span><span class="special">,</span> <span class="identifier">SI</span><span class="special">::</span><span class="identifier">force</span><span class="special">,</span> <span class="keyword">double</span><span class="special">,</span> <span class="number">3.14159265358979323846</span><span class="special">);</span>
<span class="comment">// make conversion to SI the default.</span>
<span class="identifier">BOOST_UNITS_DEFAULT_CONVERSION</span><span class="special">(</span><span class="identifier">my_unit_tag</span><span class="special">,</span> <span class="identifier">SI</span><span class="special">::</span><span class="identifier">force</span><span class="special">);</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_units.Quantities.Quantity_Construction_and_Conversion"></a><a class="link" href="Quantities.html#boost_units.Quantities.Quantity_Construction_and_Conversion" title="Construction and Conversion of Quantities">Construction
      and Conversion of Quantities</a>
</h3></div></div></div>
<p>
        This library is designed to emphasize safety above convenience when performing
        operations with dimensioned quantities. Specifically, construction of quantities
        is required to fully specify both value and unit. Direct construction from
        a scalar value is prohibited (though the static member function <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html#idp109714352-bb">from_value</a></code></span>
        is provided to enable this functionality where it is necessary. In addition,
        a <span class="underline"><code class="computeroutput"><a class="link" href="Reference.html#boost.units.quantity_cast_idp109764640">quantity_cast</a></code></span>
        to a reference allows direct access to the underlying value of a <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span>
        variable. An explicit constructor is provided to enable conversion between
        dimensionally compatible quantities in different unit systems. Implicit conversions
        between unit systems are allowed only when the reduced units are identical,
        allowing, for example, trivial conversions between equivalent units in different
        systems (such as SI seconds and CGS seconds) while simultaneously enabling
        unintentional unit system mismatches to be caught at compile time and preventing
        potential loss of precision and performance overhead from unintended conversions.
        Assignment follows the same rules. An exception is made for quantities for
        which the unit reduces to dimensionless; in this case, implicit conversion
        to the underlying value type is allowed via class template specialization.
        Quantities of different value types are implicitly convertible only if the
        value types are themselves implicitly convertible. The <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span> class also defines
        a <code class="computeroutput"><span class="identifier">value</span><span class="special">()</span></code>
        member for directly accessing the underlying value.
      </p>
<p>
        To summarize, conversions are allowed under the following conditions :
      </p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
            implicit conversion of <code class="computeroutput"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span></code> to <code class="computeroutput"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Z</span><span class="special">&gt;</span></code> is allowed if <code class="computeroutput"><span class="identifier">Y</span></code>
            and <code class="computeroutput"><span class="identifier">Z</span></code> are implicitly
            convertible.
          </li>
<li class="listitem">
            assignment between <code class="computeroutput"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span></code> and <code class="computeroutput"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Z</span><span class="special">&gt;</span></code> is allowed if <code class="computeroutput"><span class="identifier">Y</span></code>
            and <code class="computeroutput"><span class="identifier">Z</span></code> are implicitly
            convertible.
          </li>
<li class="listitem">
            explicit conversion between <code class="computeroutput"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit1</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span></code> and <code class="computeroutput"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit2</span><span class="special">,</span><span class="identifier">Z</span><span class="special">&gt;</span></code> is allowed if <code class="computeroutput"><span class="identifier">Unit1</span></code>
            and <code class="computeroutput"><span class="identifier">Unit2</span></code> have the same
            dimensions and if <code class="computeroutput"><span class="identifier">Y</span></code> and
            <code class="computeroutput"><span class="identifier">Z</span></code> are implicitly convertible.
          </li>
<li class="listitem">
            implicit conversion between <code class="computeroutput"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit1</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span></code> and <code class="computeroutput"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit2</span><span class="special">,</span><span class="identifier">Z</span><span class="special">&gt;</span></code> is allowed if <code class="computeroutput"><span class="identifier">Unit1</span></code>
            reduces to exactly the same combination of base units as <code class="computeroutput"><span class="identifier">Unit2</span></code> and if <code class="computeroutput"><span class="identifier">Y</span></code>
            and <code class="computeroutput"><span class="identifier">Z</span></code> are convertible.
          </li>
<li class="listitem">
            assignment between <code class="computeroutput"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit1</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span></code> and <code class="computeroutput"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit2</span><span class="special">,</span><span class="identifier">Z</span><span class="special">&gt;</span></code> is allowed under the same conditions
            as implicit conversion.
          </li>
<li class="listitem">
            <code class="computeroutput"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span></code>
            can be directly constructed from a value of type <code class="computeroutput"><span class="identifier">Y</span></code>
            using the static member function <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html#idp109714352-bb">from_value</a></code></span>.
            Doing so, naturally, bypasses any type-checking of the newly assigned
            value, so this method should be used only when absolutely necessary.
          </li>
</ul></div>
<p>
        Of course, any time implicit conversion is allowed, an explicit conversion
        is also legal.
      </p>
<p>
        Because dimensionless quantities have no associated units, they behave as
        normal scalars, and allow implicit conversion to and from the underlying
        value type or types that are convertible to/from that value type.
      </p>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2003-2008 Matthias Christian Schabel<br>Copyright &#169; 2007-2010 Steven
      Watanabe<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
</div></td>
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